Coherence & Light • Two waves coherent if fixed phase relationship between them for some period of time

Coherence • Coherence appear in two ways Spatial Coherence • Waves in phase in time, but at different points in space • Required for interference and diffraction • Before lasers need to place slits far from source or pass light through slit so only part of source seen Temporal Coherence • Correlation of phase at the same point but at different times • Regular sources rapidly change phase relationships • Single atom on 10-8 sec coherent lifetime of atom in an excited state • Much shorter for groups of atoms • For lasers in single mode much longer time

Coherence Length and Time • Time of coherence given by τcoh • Coherence time about time taken for photon to pass a given distance (Coherence length) in space • Coherence length is

cohcoh cL τ=

• Best seen in Michelson-Morley experiment • Beam is split into two beam paths, reflected and combine • If get interference pattern then within Coherence lengths • Before lasers paths needed to be nearly equal • With lasers only require

( ) coh21 LLL2 <−

• Coherence last 50 - 100 m with lasers

Coherence Length and Lasers • As the coherence length is

cohcoh cL τ=

• If want interference distances < coherence length • Lasers have high coherence • It can be shown Coherence time related to laser frequency width Δν (linewidth)

ντ

Δ=

1coh

Example of Coherence Length Sodium vapour lamp yellow "D" line • λ = 589 nm and linewidth 5.1x1011 Hz • Thus coherence time and length is

sec10x96.110x1.511 12

11coh−==

Δ=

ντ

( ) mm59.0m10x88.510x96.110x98.2cL 4128cohcoh ==== −−τ

• Coherence small hence hard to create holograms • HeNe laser in multimode operation • λ = 632.8 nm and linewidth 1500 MHz • Thus coherence time and length is

sec10x67.610x5.1

11 109coh

−==Δ

=ν

τ

( ) m2.010x67.610x98.2cL 108cohcoh === −τ

• If single mode HeNe operation linewidth goes to 1 Mz and cohrence time is 1 microsec, cohrence length 300 m

Fourier Domain Optical Coherence Tomography

(FD OCT)

Marinko V. Sarunic, Ph. D.Assistant Professor

School of Engineering ScienceSimon Fraser University

msarunic@sfu.ca(604) 268 7654

Common Patient Imaging ModalitiesImaging Method Resolution

PenetrationDepth

Source of contrast Cost

Computed Tomography(X-rays)

2 – 3 mm Entire body Attenuation $$$

MagneticResonanceImaging

2 – 3 mm Entire body [ H+ ] $$$$

Ultrasound 500 μm 10 – 20 cm Acoustic scattering

$$

Visual Examination 100 μm Surface Natural Colouring $

Coherence Domain Optical Imaging 1 – 10 μm 2 – 3 mm

Optical scattering & absorption

$$

Histology 1 μm 5 – 10 μmsections

Histological stains $$

Modified from J.A. Izatt, OCT Short Course

Optical Coherence Tomography • In tissue shortest path photons are least scattered• Consider starting with a coherent source (laser)• 2 paths: one to tissue, other to reference• Use Michelson interferometer methods• By adjusting reference delay scan return in phase• Hence can separate scattered from unscattered• Called Time Domain OCT

Optical Coherence Tomography

Transverse Resolution:

Longitudinal Resolution:Low-Coherence

Source

Detector

50/50

Sample

Demodulator AD

Interferometric Data A-Scans B-Scan

Computer

Reference

B-scanB-scan: log scale imageAxial A-scan

Log scale intensity (dB)

Dep

thm~

n2ln2l

2

c

μλΔ

λπ

151.5 −

=

μm~.A.N2

22.1x

25 - 2

λΔ =

Ophthalmic Optical Coherence Tomography

CorneaCornea

AqueousAqueous

LensLens

IrisIris

ScleraSclera

Log Reflection Log Reflection 4 mm4 mm

Anterior SegmentIzatt, et. al., Arch. Ophthalmol. 112:1584-1589, 1994.

Log ReflectionLog Reflection

Optic DiskOptic DiskFoveaFovea

RNFLRNFL

ChoroidChoroid

VitreousVitreous

ScleraSclera

250 µm250 µm

250 µm

RetinaHee, et. al., Arch. Ophthalmol. 113:325-332, 1995.

Esophagus

IN VIVO HUMAN ENDOSCOPIC OCT

Stomach

Small Intestine

Colon

Rectum

J.A. Izatt, OCT Short Course

B – Barrett’s EsophagusA – Adenocarcinoma

CANCER IMAGING WITH ENDOSCOPIC OCTInvasive Adenocarcinoma in Barrett’s Esophagus

1 mm

BA

J.A. Izatt, OCT Short Course

Cardiac Morphology And Cardiac Morphology And Development In Chick EmbryosDevelopment In Chick Embryos

Yelbuz, et.al., Circulation 106: 2771, 2002

Heart tube folding

A B

C D E F

v

CJ

m

IC

OC

en

i

oo

v

IC

OC

i

i

v

o

iv

o

o

i

viv

o

v

CJ

m

IC

OC

en

i

oo

v

IC

OC

i

i

v

o

iv

o

o

i

viv

o

v

CJ

m

IC

OC

en

i

oo

v

IC

OC

i

i

v

o

iv

o

o

i

viv

o

A B

C D E F

A B

C D E F

Balance Sheet for OCT

• Non-Contact Measurement• High resolution: 10 - 20 µm in 3

dimensions• Compact, Inexpensive Diode-

Fiber System• Compatible with Existing

Medical Instrumentation

• Speed limited by maximum optical exposure

– Particularly important in ophthalmic imaging

» MPE < 770 μW @ 830 nm » MPE < 15.4 mW @ 1310 nm

• High speed systems require complicated rapid scanning optical delay line (RSOD)

• Axial resolution trade-off with sensitivity

• Maximum tissue depth of ~2mm

Fourier Domain OCT• Time domain OCT: reference moves• Fourier Domain: reference fixed• Now look at frequency (wavelength) changesSpectral Domain• Diffraction grating spreads spectrum• Different λ different phase• Use array type detectorSwept Source • Sweep Laser source (narrow line)• Encode spectrum in time

Fourier Domain OCT

• Fixed reference arm• Interferogram acquired as

function of wavenumber

Sample

Low coherencesource 2x2 Fiber

couplerDiffractiongrating

Array detector

λ1λn

Sample

Wavelengthswept laser 2x2 Fiber

coupler

Photodiodedetector

SD OCT

SS OCT

))zk2cos(RR2RR(]k[S]k[D mSRSRmmi Δ++⋅∝

k

FT

x

( )[( ) ( )( )]zzzzRR2

)z(RR]z[S]z[D

nnSR

nSRnni

ΔδΔδ

δ

−+++

+⊗∝ K

Fixed reference

Fixed referenceDC peak

Symmetricsignal peaks

Complex conjugate artifact

High Resolution Retinal FDOCTInner retinal layers FoveaBlood vessels

RNFL

RPEOptic Nerve Head

Acquisition Parameters: • 1000 A-scans/B-scan• 50μs A-scan int. time

(20 kHz)• 17 frames/sec display• 11mm lateral scan•λo=841 nm, Δλ=49nm

B.A. Bower, SPIE Photonics West, 2006

Compare to commercial TD OCT results

High Speed Volumetric Retinal FDOCT

Retinal image from fundus camera

- white light- CCD camera

Scan Location

Summed voxel projection from raster canned OCT Data: “OCT Fundus” Image

B.A. Bower, SPIE Photonics West, 2006

Small Animal Imaging

Bioptigen, Inc. OCT Microscope

• λo=1300 nm, • Δλ=70nm • LPS: 6-24 kHz• FPS: 6-24 Hz• Volume: 4-25 s• Flow measurement

using Doppler processing

• Video light microscopy, SEM, confocal microscopy often inadequate for quantitative measurements.

• OCT is uniquely suited to image popular small model organisms such as fruit fly, chick embryo, zebrafish, and xenopus

- 2.5

0

2.5

5.0

7.5

- 5.0

-

-time (ms)

1000 2000 3000 4000 5000

Vel

ocity

(mm

/s)

Chick embryo Cardiac Doppler flow measurement

SLD

50/50

ref arm

pc

spectrometer

A.M. Davis, OSA Biomed. Topical Meeting, 2006

CCDDG

Limited Sample Depth FD OCT: Imaging the Human Eye

• Posterior Segment– Retina, macula, optic nerve head– Structures < 1 mm thick

• Anterior chamber– Cornea, iris, crystalline lens– > 6 mm sample depth required

www.webvision.med.utah.edu/ imageswv/sagitta2.jpeg

2mm

Reference mirror virtual position

4mm

Reference mirror virtual position

High Speed Complex Conjugate Resolved Ocular Anterior Segment Images

• Average all three detector signals

– Image corrupted by complex conjugate artifact

• Quadratureprojection processing

– Complex conjugate resolved images Iris Angle

Limbus

Sclera

Cornea

DC artifact

Epithelium

Ciliary bodyCrystalline lens